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A reduced bias method of estimating variance components in generalized linear mixed models
In small samples it is well known that the standard methods for estimating variance components in a generalized linear mixed model (GLMM), pseudo-likelihood and maximum likelihood, yield estimates that are biased downward. An important consequence of this is that inferences on fixed effects will have inflated Type I error rates because their precision is overstated. We introduce a new method for estimating parameters in GLMMs that applies a Firth bias adjustment to the maximum likelihood-based GLMM estimating algorithm. We apply this technique to one- and two-treatment logistic regression models with a single random effect. We show simulation results that demonstrate that the Firth-adjusted variance component estimates are substantially less biased than maximum likelihood estimates and that inferences using the Firth estimates maintain their Type I error rates more closely than the standard methods.
Claassen, Elizabeth A, "A reduced bias method of estimating variance components in generalized linear mixed models" (2014). ETD collection for University of Nebraska - Lincoln. AAI3618588.